Jordan Triple Systems by the Grid Approach

1987
ISBN: 978-3-540-18362-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1280, 194 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g

Reihe: Lecture Notes in Mathematics

Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are - classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs - a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface - structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

Zielgruppe

Research

Autoren/Hrsg.

Neher, Erhard

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Special families of compatible tripotents.- Classification of grids.- Coordinatization theorems.- Classifications.